Improper Integrals on 42 platforms
01-20-2019, 06:48 PM
Post: #1
 lrdheat Senior Member Posts: 645 Joined: Feb 2014
Improper Integrals on 42 platforms
I was grateful to have been generously given an HP-42S. I was quite impressed, and ordered the DM 42. I'm wondering...has anyone noticed that the 42S and the DM 42 seem to have difficulty with improper integrals? I tried integrating (abs(sin x))/x from -pi/4 to pi/3, and found that even on the DM 42, I had to give up when using acc=1E-5. It did better at acc=1E-03. In contrast, my new TI 30X Pro MathPrint with the default at 1E-05 comes up with an answer good through 5 decimals in 28 seconds. On proper integrals, the various 42's are faster, the DM 42 often very quick. Still, I find that I like the feel of the 42S and it's keyboard. The DM 42 keyboard annoyingly will miss a keystroke from time to time...
01-20-2019, 08:40 PM
Post: #2
 Thomas Klemm Senior Member Posts: 1,447 Joined: Dec 2013
RE: Improper Integrals on 42 platforms
I assume that the problem is rather related to the discontinuity at $$x=0$$ than the division by $$0$$.

You can try to integrate:

$$\int_{-\frac{\pi}{4}}^{\frac{\pi}{3}}\frac{\left |x \right |}{x}dx$$

Use the following program and you will probably have the same experience:
Code:
00 { 15-Byte Prgm } 01▸LBL "f(x)" 02 MVAR "x" 02 RCL "x" 04 SIGN 05 END

You can speed things up if you split your integral into two parts:

$$\int_{-\frac{\pi}{4}}^{\frac{\pi}{3}}\frac{\left |\sin x \right |}{x}dx=\int_{-\frac{\pi}{4}}^{0}\frac{\left |\sin x \right |}{x}dx+\int_{0}^{\frac{\pi}{3}}\frac{\left |\sin x \right |}{x}dx$$

I haven't tried this using the HP-42S but it works with the Free42.

HTH
Thomas
01-21-2019, 05:56 PM (This post was last modified: 01-21-2019 06:01 PM by Albert Chan.)
Post: #3
 Albert Chan Senior Member Posts: 1,593 Joined: Jul 2018
RE: Improper Integrals on 42 platforms
(01-20-2019 08:40 PM)Thomas Klemm Wrote:  You can speed things up if you split your integral into two parts:

$$\int_{-\frac{\pi}{4}}^{\frac{\pi}{3}}\frac{\left |\sin x \right |}{x}dx=\int_{-\frac{\pi}{4}}^{0}\frac{\left |\sin x \right |}{x}dx+\int_{0}^{\frac{\pi}{3}}\frac{\left |\sin x \right |}{x}dx$$

Or, remove the discontinuity: integ(sin(x)/x, x, pi/4, pi/3) ~ 0.226483
01-21-2019, 06:01 PM
Post: #4
 Csaba Tizedes Senior Member Posts: 490 Joined: May 2014
RE: Improper Integrals on 42 platforms
(01-20-2019 06:48 PM)lrdheat Wrote:  my new TI 30X Pro MathPrint
I'll be a little OFF, but could you start a topic for this calculator? I am very interested but not so much information available yet from users.

Thanks,
Csaba
01-21-2019, 08:58 PM
Post: #5
 lrdheat Senior Member Posts: 645 Joined: Feb 2014
RE: Improper Integrals on 42 platforms
It's an updated 36X Pro, essentially identical, but at least twice as fast, more generous on how many characters can be accepted in a MathPrint mode equation, 3 data lists can handle 50 entries, up from 42 on the 36X Pro. 3 new regressions are available: a*x, a/x + b, a*e^ (b*x). No auto "best choice" as offered by some HP's. Display is easier to read.
01-21-2019, 09:06 PM
Post: #6
 ijabbott Senior Member Posts: 1,023 Joined: Jul 2015
RE: Improper Integrals on 42 platforms
(01-21-2019 08:58 PM)lrdheat Wrote:  It's an updated 36X Pro, essentially identical, but at least twice as fast, more generous on how many characters can be accepted in a MathPrint mode equation, 3 data lists can handle 50 entries, up from 42 on the 36X Pro. 3 new regressions are available: a*x, a/x + b, a*e^ (b*x). No auto "best choice" as offered by some HP's. Display is easier to read.

And no silver keys!

— Ian Abbott
01-21-2019, 09:14 PM
Post: #7
 ijabbott Senior Member Posts: 1,023 Joined: Jul 2015
RE: Improper Integrals on 42 platforms
(01-21-2019 06:01 PM)Csaba Tizedes Wrote:
(01-20-2019 06:48 PM)lrdheat Wrote:  my new TI 30X Pro MathPrint
I'll be a little OFF, but could you start a topic for this calculator? I am very interested but not so much information available yet from users.

Thanks,
Csaba

There are quite a few posts about the Pro MathPrint in the thread TI-36X Pro—Replace the batteries or just get a new one? from post #19 onwards.

— Ian Abbott
01-21-2019, 10:51 PM
Post: #8
 lrdheat Senior Member Posts: 645 Joined: Feb 2014
RE: Improper Integrals on 42 platforms
Another observation: Many of the constants have been updated on the 30X Pro MathPrint since the 36X Pro...
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